At the hospital, Fran Sr. and Ray are in a restroom. Fran washes his hands and struggles a bit to reach in and pull a paper towel from the dispenser. Four or five times the camera cuts back from Ray to Fran and the dispenser alternately has the towels hanging out, then tucked in, then hanging out again.
In the scene where Ray is staking out the junkie informant in the Santa hat to find Tezo, when he he jumps out of the car and starts running, he has an empty, unsnapped and flapping holster on his left hip (rear view) but is not carrying a weapon in his hand. When we next see him, he has the holster on his right hip, gun in it and snapped closed. He then un-holsters his weapon from that left hip holster when he readies to enter the building.
Where Raymond and Francis, Sr. are in the bathroom, Francis urges Raymond to join the Task Force. Francis removes towels from the dispenser. In the next two subsequent shots, the position of the towels at the dispenser has changed.
When Francis arrives at the initial crime scene, he tells Billy to hang on as the ambulance is wheeling him out. Billy has a non-re-breather mask on, but no oxygen is being administered because the bag on the mask is deflated.
When Colin Farrell threatens to burn the baby, he says it has severe "1st degree burns", but he means "3rd degree burns". A plausible explanation is that in Law Enforcement, the lower the number on the charge means the most severe, (1st degree theft more severe than 3rd). It's the opposite for burn terminology.